CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. In addition, the CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This paper provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM paper in 1983.
element, namely, the choice of the reaction coordinate for determining the free energy of activation to characterize the mechanism of enzymatic processes. Then, we illustrate a variety of factors that have been found to contribute to catalysis in specific enzymatic reactions by lowering the free energy of activation relative to that for the uncatalyzed process in aqueous solution. Finally, we provide a summary of the major conclusions. 2. Methods for Computational Studies of Enzymatic Reactions in Aqueous Solution In this section, we present a brief summary of the theory and key computational techniques that we use for studying chemical reactions catalyzed by enzymes and the corresponding uncatalyzed reactions, both in aqueous solution. 2.1. Generalized Transition State Theory Generalized transition state theory (TST) provides a theoretical framework for understanding chemical reactions in the gas phase, in solution, and in enzymes. Conventional 24,25 and generalized 26 transition state theory were originally developed for gas-phase reactions, but transition state theory is readily generalized to liquid-phase reactions, 27 and it has become the framework for both qualitative and quantitative studies of reactions catalyzed by enzymes. The rate constant for a reaction at temperature T can be conveniently expressed as follows: (1) where β = 1/(k B T), k B being Boltzmann's constant, h is Planck's constant, and k TST is the transition state theory rate constant. The transmission coefficient, γ(T), which has a value of unity in simple transition state theory, has three components, 7 (2) which account for, respectively, dynamical recrossing of the transition state hypersurface that separates the reactants and products, quantum mechanical tunneling in the reaction coordinate, and nonequilibrium distributions in phase space. Note that γ(T), κ(T), and Γ(T) are called, respectively, the transmission coefficient, the tunneling transmission coefficient, and the recrossing transmission coefficient. In eq 1, ΔG ‡ (T) is the molar standard-state quasithermodynamic free energy of activation, which is related to the potential of mean force, W(T,q), also called the PMF, by eq 3, 28,29 (3) where q ‡ and q R are values of the reaction coordinate, q, at the transition state and reactant state, respectively, G R (q) corresponds to the free energy of the mode in the reactant state, R, which correlates with the reaction coordinate, and C(T,q) is a correction term that is due to the Jacobian of the transformation from a locally rectilinear reaction coordinate to the Gao et al.
The H/D primary kinetic isotope effect (KIE) for the hydride transfer reaction catalyzed by Escherichia coli dihydrofolate reductase (ecDHFR) is calculated as a function of temperature employing ensemble-averaged variational transition-state theory with multidimensional tunneling. The calculated KIEs display only a small temperature dependence over the temperature range of 5 to 45 °C. We identify two key features that contribute to canceling most of the temperature dependence of the KIE that would be expected on the basis of simpler models. Related issues such as the isotope effects on Arrhenius preexponential factors, large differences between free energies of activation and Arrhenius activation energy, and fluctuations of effective barriers are also discussed. This paper presents a theoretical explanation of the unusual temperature dependence 1 of the kinetic isotope effect (KIE) for the hydride transfer chemical step of the reaction catalyzed by E. coli dihydrofolate reductase (ecDHFR). The explanation identifies two general features that may be important in interpreting enzymatic kinetic isotope effects more generally.Many enzyme reactions involve hydron transfer (transfer of H + , H − , or H • ). Such reactions have significant contributions from zero-point energy and tunneling; KIEs have been extensively used to study these effects.  Surprisingly, a number of enzymes have been found to display almost temperature-independent KIEs, 1-4 which are contrary to experience with small-molecule chemistry or simple tunneling models. Recent multidimensional tunneling calculations have been successfully used to study tunneling effects on enzymatic KIEs, but the most accurate methods have so far been applied only at a single temperature. 8 DHFR catalyzes the reduction of 7,8-dihydrofolate (DHF) to 5,6,7, with the key chemical step being the transfer of a hydride ion from the nicotinamide ring of the cofactor nicotinamide adinine dinucleotide phosphate (NADPH). At pH ≅ 7, product release is partly rate-limiting 9 and the H/D kinetic isotope effect is about 1.1-1.3, but the intrinsic KIE on the hydride transfer step is >3. 10 Furthermore, at 25 °C, the phenomenological free energy of activation derived from the rate constant 9 by using © 2005 American Chemical Society HHS Public Access Author Manuscript Author ManuscriptAuthor ManuscriptAuthor Manuscript transition-state theory is 13.4 kcal/mol, 7 and the free energy of reaction calculated from the experimental equilibrium constant 9 is −4.4 kcal/mol. 7Here, we report a dynamical simulation of the ecDHFR system using a combined quantum mechanical and molecular mechanical (QM/MM) approach. As depicted in Figure 1, the reactive fragment that involves transferring a hydride ion from the C4 position of NADPH (the cofactor) to the C6 in N5-preprotonated DHF (the substrate) to form THF (the product) is treated quantum mechanically. The hydride transfer KIEs at 5 and 45 °C and 1 atm are calculated using ensemble-averaged variational transition-stat...
We report tests of second-and third-generation density functionals, for pure density functional theory (DFT) and hybrid DFT, against the BH6 representative barrier height database and the AE6 representative atomization energy database, with augmented, polarized double and triple zeta basis sets. The pure DFT methods tested are G96LYP, BB95, PBE, mPWPW91, VSXC, HCTH, OLYP, and OPW91 and the hybrid DFT methods tested are B1B95, PBE0, mPW1PW91, B97-1, B98, MPW1K, B97-2, and O3LYP. The performance of these methods is tested against each other as well as against firstgeneration methods (BP86, BLYP, PW91, B3PW91, and B3LYP). We conclude that the overall performance of the second-generation DFT methods is considerably better than the first-generation methods. The MPW1K method is very good for barrier height calculations, and none of the pure DFT methods outperforms any of the hybrid DFT methods for kinetics. The B1B95, VSXC, B98, OLYP and O3LYP methods perform best for atomization energies. Using a mean mean unsigned error criterion (MMUE) that involves two sizes of basis sets (both with polarization and diffuse functions) and averages mean unsigned errors in barrier heights and in atomization energy per bond, we find that VSXC has the best performance among pure functionals, and B97-2, MPW1K, and B1B95 have the best performance of all hybrid functionals tested.y Electronic supplementary information (ESI) available: Mean errors for pure and hybrid DFT methods. See
The generalized hybrid orbital (GHO) method provides a way to combine quantum mechanical (QM) and molecular mechanical (MM) calculations on a single molecular system or supramolecular assembly by providing an electrostatically stable connection between the QM portion and the MM portion. The GHO method has previously been developed for semiempirical molecular orbital calculations, on the basis of neglect of diatomic differential overlap (GHO−NDDO); in the present work, it is extended to the ab initio Hartree−Fock (HF) level (GHO−AIHF). First, the theoretical foundation for the GHO−AIHF extension is discussed, and four different approaches are proposed to overcome the nonorthogonality between active molecular orbitals (MOs) and auxiliary MOs. In the first scheme, the auxiliary hybrid basis functions are projected out of the active QM basis. The second scheme neglects the diatomic differential overlap between the auxiliary basis and the active QM basis. In the third scheme, hybrid orbitals are constructed from Löwdin-type symmetric orthogonalized atomic orbitals on the basis of global Löwdin orthogonalization. The fourth procedure involves local Löwdin orthogonalization. The procedures for implementing the four GHO−AIHF schemes are described, and analytical gradient expressions are derived. The unparametrized GHO−AIHF method is tested for hydrocarbons with various basis sets, in particular, the geometries and charges are compared with pure QM calculations for ethane, ethyl radical, and n-octane, and the method is tested for the torsion potential around the central bond in n-butane. Furthermore, a parametrization of the GHO−AIHF method for the MIDI! basis is presented and tested for 16 molecules and ions with various functional groups near the QM/MM boundary. The results show the robustness of the algorithm and illustrate the significant improvement made by introducing several one-electron integral-scaling parameters. Finally, the energetic performance of the method is tested by comparing the proton affinities for a set of small model compounds (alcohols, amines, thiols, and acids) to results obtained from fully QM calculations. We conclude that the GHO−AIHF scheme provides a reasonable fundamental solution to the problem of combining an ab initio quantum mechanical electronic structure calculation with molecular mechanics.
It has been suggested that the magnitudes of secondary kinetic isotope effects (2 degrees KIEs) of enzyme-catalyzed reactions are an indicator of the extent of reaction-center rehybridization at the transition state. A 2 degrees KIE value close to the corresponding secondary equilibrium isotope effects (2 degrees EIE) is conventionally interpreted as indicating a late transition state that resembles the final product. The reliability of using this criterion to infer the structure of the transition state is examined by carrying out a theoretical investigation of the hybridization states of the hydride donor and acceptor in the Escherichia coli dihydrofolate reductase (ecDHFR)-catalyzed reaction for which a 2 degrees KIE close to the 2 degrees EIE was reported. Our results show that the donor carbon at the hydride transfer transition state resembles the reactant state more than the product state, whereas the acceptor carbon is more productlike, which is a symptom of transition state imbalance. The conclusion that the isotopically substituted carbon is reactant-like disagrees with the conclusion that would have been derived from the criterion of 2 degrees KIEs and 2 degrees EIEs, but the breakdown of the correlation with the equilibrium isotope effect can be explained by considering the effect of tunneling.
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